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Outlier Detection And Estimation In NonLinear Time Series

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  • Francesco Battaglia
  • Lia Orfei

Abstract

. The problem of identifying the time location and estimating the amplitude of outliers in nonlinear time series is addressed. A model‐based method is proposed for detecting the presence of additive or innovational outliers when the series is generated by a general nonlinear model. We use this method for identifying and estimating outliers in bilinear, self‐exciting threshold autoregressive and exponential autoregressive models. A simulation study is performed to test the proposed procedures and comparing them with the methods based on linear models and linear interpolators. Finally, our results are applied for detecting outliers in the Canadian lynx trappings and in the sunspot numbers data.

Suggested Citation

  • Francesco Battaglia & Lia Orfei, 2005. "Outlier Detection And Estimation In NonLinear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 107-121, January.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:1:p:107-121
    DOI: 10.1111/j.1467-9892.2005.00392.x
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    References listed on IDEAS

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    1. Chen, Cathy W. S., 1997. "Detection of additive outliers in bilinear time series," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 283-294, May.
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    4. Wai-Sum Chan, 1995. "Understanding the effect of time series outliers on sample autocorrelations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 179-186, June.
    5. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    6. M. M. Gabr & T. Subba Rao, 1981. "The Estimation And Prediction Of Subset Bilinear Time Series Models With Applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(3), pages 155-171, May.
    7. Ledolter, Johannes, 1989. "The effect of additive outliers on the forecasts from ARIMA models," International Journal of Forecasting, Elsevier, vol. 5(2), pages 231-240.
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    Cited by:

    1. Ping Chen & Jing Yang & Linyuan Li, 2015. "Synthetic detection of change point and outliers in bilinear time series models," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(2), pages 284-293, January.
    2. Sadahiro, Yukio, 2021. "A method for analyzing the daily variation in the spatial pattern of market area," Journal of Retailing and Consumer Services, Elsevier, vol. 58(C).
    3. Olivier Darné & Amélie Charles, 2011. "Large shocks in U.S. macroeconomic time series: 1860-1988," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 5(1), pages 79-100, January.
    4. Luigi Grossi & Fany Nan, 2017. "Forecasting electricity prices through robust nonlinear models," Working Papers 06/2017, University of Verona, Department of Economics.
    5. Battaglia, Francesco, 2005. "Outliers in functional autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 323-332, May.
    6. Giordani, Paolo & Kohn, Robert & van Dijk, Dick, 2007. "A unified approach to nonlinearity, structural change, and outliers," Journal of Econometrics, Elsevier, vol. 137(1), pages 112-133, March.
    7. Kocenda, Evzen & Valachy, Juraj, 2006. "Exchange rate volatility and regime change: A Visegrad comparison," Journal of Comparative Economics, Elsevier, vol. 34(4), pages 727-753, December.
    8. Luigi Grossi & Fany Nan, 2018. "The influence of renewables on electricity price forecasting: a robust approach," Working Papers 2018/10, Institut d'Economia de Barcelona (IEB).
    9. Hamid Louni, 2008. "Outlier detection in ARMA models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1057-1065, November.
    10. Grossi, Luigi & Nan, Fany, 2019. "Robust forecasting of electricity prices: Simulations, models and the impact of renewable sources," Technological Forecasting and Social Change, Elsevier, vol. 141(C), pages 305-318.

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